This paper concerns the staffing optimization problem in multi-skill call centers. The objective is to find a minimal cost staffing solution while meeting a target level for the quality of service (QoS) to customers. We consider a staffing problem in which joint chance constraints are imposed on the QoS of the day. Our joint chance-constrained formulation is more rational capturing the correlation between different call types, as compared to separate chance-constrained versions considered in previous studies. We show that, in general, the probability functions in the joint-chance constraints display S-shaped curves, and the optimal solutions should belong to the concave regions of the curves. Thus, we propose an approach combining a heuristic phase to identify solutions lying in the concave part and a simulation-based cut generation phase to create outer-approximations of the probability functions. This allows us to find good staffing solutions satisfying the joint-chance constraints by simulation and linear programming. We test our formulation and algorithm using call center examples of up to 65 call types and 89 agent groups, which shows the benefits of our joint-chance constrained formulation and the advantage of our algorithm over standard ones.

本文关注多技能呼叫中心的人员配置优化问题。目标是找到成本最低的人员配备解决方案，同时满足客户服务质量 (QoS) 的目标水平。我们考虑一个人员配备问题，其中联合机会约束被施加在当天的 QoS 上。与先前研究中考虑的单独机会约束版本相比，我们的联合机会约束公式更合理地捕捉了不同呼叫类型之间的相关性。我们表明，一般情况下，联合机会约束中的概率函数呈现 S 形曲线，最优解应该属于曲线的凹区域。因此，我们提出了一种结合启发式阶段来识别位于凹面部分的解决方案和基于模拟的切割生成阶段来创建概率函数的外部近似的方法。这使我们能够通过模拟和线性规划找到满足联合机会约束的良好人员配备解决方案。我们使用多达 65 种呼叫类型和 89 个座席组的呼叫中心示例测试我们的公式和算法，这显示了我们的联合机会约束公式的好处以及我们的算法相对于标准公式的优势。